(D) Given: Velocity $v = 10\,m/s$,Frequency $f = 100\,Hz$,Path difference $\Delta x = 2.5\,cm = 0.025\,m$.First,calculate the wavelength $\lambda$ usi

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(D) Given: Velocity $v = 10\,m/s$,Frequency $f = 100\,Hz$,Path difference $\Delta x = 2.5\,cm = 0.025\,m$.First,calculate the wavelength $\lambda$ using the relation $v = f\lambda$:$\lambda = \frac{v}{f} = \frac{10}{100} = 0.1\,m = 10\,cm$.Now,use the formula for phase difference $\Delta \phi$:$\Delta \phi = \frac{2\pi}{\lambda} \times \Delta x$.Substituting the values:$\Delta \phi = \frac{2\pi}{10\,cm} \times 2.5\,cm = \frac{2\pi}{4} = \frac{\pi}{2}$ radians.

Class 11 Physics Waves Wave Equation and Characteristics of Waves

Medium

$A$ transverse progressive wave on a stretched string has a velocity of $10\,m/s$ and a frequency of $100\,Hz$. The phase difference between two particles of the string which are $2.5\,cm$ apart will be:

A
$\frac{\pi}{8}$
B
$\frac{\pi}{4}$
C
$\frac{3\pi}{8}$
D
$\frac{\pi}{2}$

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Wave Equation and Characteristics of Waves

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$A$ transverse progressive wave on a stretched string has a velocity of $10\,m/s$ and a frequency of $100\,Hz$. The phase difference between two particles of the string which are $2.5\,cm$ apart will be:

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$A$ plane wave is represented by $x = 1.2 \sin(314t + 12.56y)$,where $x$ and $y$ are distances measured in meters and $t$ is time in seconds. This wave has:

The equations of two simple harmonic waves are given by $Y_1 = 2 \sin 8 \pi \left(\frac{t}{0.2} - \frac{x}{2}\right) \text{ m}$ and $Y_2 = 4 \sin 8 \pi \left(\frac{t}{0.16} - \frac{x}{1.6}\right) \text{ m}$. Then both waves have:

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